Constructing index numbers - aggregates method, Financial Management

Aggregates Method

Under the aggregates method of constructing an index number, we could have unweighted aggregates index and the weighted aggregates index.

Unweighted Aggregates Index

An unweighted aggregates index is calculated by totalling the current year/given year's elements and then dividing the result by the sum of the same elements during the base period. To construct a price index, the following mathematical formula may be used

Unweighted Aggregates Price Index

=

x 100

where,

=

Sum of all elements in the composite for current year

=

Sum of all elements in the composite for base year

This is the simplest method of constructing index numbers. The example demonstrates the application of an unweighted index.

Construction of Unweighted Price Index

Elements in the composite

Prices (in Rs.)

2000

2001

(P0)

(P1)

Oranges (1 dozen)

20

28

Milk (1 liter)

5

8

LPG Cylinder

76

100

101

136

Unweighted aggregates price index

=

134.65

Above we measured changes in general price levels on the basis of changes in prices of a few items. While the year 2000 was taken as the base year, a comparison has been made between the prices of 2001 and that of the base year 2000. As evident, the price index was 134.65 which means that the prices rose by 34.65 percent from 2000 to 2001. By no means should this price index be interpreted as a reflection of the price changes of all goods and services as this calculation is a rough estimate. On inclusion of other items/elements and varying weights in the composite, with 2000 as the base year and 2001 as the current year, there is every possibility that the calculated price index would be different from the price index calculated earlier. This factor can be cited as one of the drawbacks of the simple unweighted index. The unweighted index does not reflect the reality since the price changes are not linked to any usage/consumption levels. On the other hand, a weighted index attaches weights according to their significance and hence is preferred to the unweighted index.

To make this clear, let us calculate the price index with the same data provided above but by changing the milk consumption from 1 liter to 100 liters. The following table provides the calculation of the price index.

Unweighted Price Index

(Rs. in crore)

Elements in the composite

Prices (in Rs.)

2000

2001

(P0)

(P1)

Oranges (1 dozen)

20

28

Milk (100 liters)

500

800

LPG Cylinder

76

100

596

928

Unweighted aggregates price index

=

= 155.70

Merely by changing the milk consumption in the composite, the unweighted price index changed from 134.65 to 155.70. As a result of ensuring that equal importance is given to all items in the composite irrespective of the consumption, the unweighted aggregates never gained much acceptance.

An unweighted aggregates quantity index and, an unweighted aggregates value index can be calculated on similar lines as calculated for price index. A mere substitution of quantities or values for prices in the equation would suffice.